Code for reproducing "Transformer for Partial Differential Equations' Operator Learning" (paper).

Models prediction on 2D Incompressible flow

For instruction on different cases, please go the corresponding subfolder. These codes are tested under PyTorch 1.8.1 on Ubuntu 18.

The dataset for 1D Burgers (Burgers_R10.zip), 2D Darcy flow (Darcy_421.zip) can be downloaded from dataset link .
We provide our processed dataset for 2D Navier-Stokes (in .npy format) at dataset link .
The dataset for these problems are under the courtesy of FNO.

Dataset courtesy under GNN-BVP, please check the original repo for data downloading.

Dataset courtesy under MeshGraphNet, we provide our processed dataset at train/test.

Alongside the aforementioned projects that have generously shared their valuable datasets, the following repositories have also been helpful for this project.

• Galerkin Transformer: https://github.com/scaomath/galerkin-transformer
• A lot useful modules for building Transformer: https://github.com/lucidrains/x-transformers

If you find this project useful, please consider citing our work:

@article{
li2023transformer,
title={Transformer for Partial Differential Equations{\textquoteright} Operator Learning},
author={Zijie Li and Kazem Meidani and Amir Barati Farimani},
journal={Transactions on Machine Learning Research},
issn={2835-8856},
year={2023},
url={https://openreview.net/forum?id=EPPqt3uERT},
note={}
}